Lecture Notes in Logic, 36

Set Theory, Arithmetic, and Foundations of Mathematics – Theorems, Philosophies

Juliette Kennedy, Roman Kossak (Editors)

Year: 2011

ISBN-13: 9781107008045
242 pages. Hardcover.Buy now (when ordering, include the discount code ASL2016 to receive the 25% ASL member discount)

This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of Tennenbaum’s theorem in arithmetic; a number of papers on Tennenbaum phenomena in weak arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Gödel’s previously unpublished 1972‑1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin’s paper arguing against the generic multiverse view; Anne Troelstra’s history of intuitionism through 1991; and Aki Kanamori’s history of the Suslin problem in set theory. The book provides a historical and philosophical treatment of particular theorems in arithmetic and set theory, and is ideal for researchers and graduate students in mathematical logic and philosophy of mathematics.

Table of Contents

Introduction Juliette Kennedy and Roman Kossak

Historical remarks on Suslin’s problem Akihiro Kanamori

The continuum hypothesis, the generic-multiverse of sets, and the Ω conjecture W. Hugh Woodin

ω-Models of finite set theory Ali Enayat, James H. Schmerl and Albert Visser

Tennenbaum’s theorem for models of arithmetic Richard Kaye

Hierarchies of subsystems of weak arithmetic Shahram Mohsenipour

Diophantine correct open induction Sidney Raffer

Tennenbaum’s theorem and recursive reducts James H. Schmerl

History of constructivism in the 20th century A. S. Troelstra

A very short history of ultrafinitism Rose M. Cherubin and Mirco A. Mannucci

Sue Toledo’s notes of her conversations with G�del in 1972�1975 Sue Toledo